diff --git a/main.ipynb b/main.ipynb index ef87ae9..5d23cf8 100644 --- a/main.ipynb +++ b/main.ipynb @@ -4,7 +4,27 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# OLS Ordinary Least Squares\n", + "# Ordinary Least Squares\n", + "\n", + "## Introduction\n", + "\n", + "The Ordinary Least Squares (OLS) is an important method in machine learning and statistics for several reasons. The OLS is a straightforward and easy-to-understand method for fitting linear models. \n", + "\n", + "The model minimizes the sum of squared differences between the observed $y$ and predicted values $\\hat{y}$, making it intuitive to understand. \n", + "\n", + "Additionally, the OLS is the foundation for linear regression, one of the most widely used machine learning and statistics techniques. Linear regression is valuable for modeling relationships between variables when you suspect a linear relationship exists.\n", + "\n", + "While OLS is valuable in many scenarios, it's essential to acknowledge its limitations, especially when dealing with nonlinear relationships or complex data structures. \n", + "\n", + "More advanced machine learning techniques like decision trees, neural networks, or support vector machines may be more appropriate in such cases. However, OLS remains a foundational method with enduring relevance in machine learning and statistics.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Obtaining the OLS general equation\n", "\n", "The OLS general model $\\hat{y}$ is defined by: \n", "\n", @@ -12,7 +32,7 @@ "\n", "Applying the partial derivatives with rescpect $\\theta_0$ and equaliting to zero:\n", "\n", - "$$\\frac{\\partial SSR}{\\partial \\theta_0}=0 $$\n", + "$$\\frac{\\partial SSR(\\theta_0, \\theta_1)}{\\partial \\theta_0}=0 $$\n", "\n", "here SSR is defined as:\n", "\n", @@ -45,12 +65,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Implementing OLS in Python" + "## Implementing OLS in Python" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -62,7 +82,7 @@ " 12.00413684, 12.54005263, 13.07596842, 13.61188421, 14.1478 ])" ] }, - "execution_count": 1, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -78,12 +98,12 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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hAwBISvgAAJISPgCApIQPACAp4QMASEr4gDmw/kqz2cxKgGEgfECBNRqNUCqVQrVazcq4DzBoVrWFgoo9HTFwdDqdqWNjY2NhYmLCYnDAQO/fej6goFqtVk/wiNrtdhgfHx9YnQAi4QMKqlKphNHR3o947Pkol8sDqxNAJHxAQcWhlXq9ngWOKJa1Ws2QCzBw5nzAHJj7EYdaYo+H4AEUcs5HHFN+3/veF5YuXRpOPPHE8LznPS/cdNNNYcgyDswZMXAsW7ZM8ACGxrx+/wtvvvnmcNttt4W//uu/Duedd17YunVreNvb3paloWuvvbbfPw4AmOvh47777gtXXHFFWLlyZbZ/7rnnhi9+8Yvhhz/8Yb9/FACQQ30fdnn1q18d7rnnnvCTn/wk2/+Xf/mX8P3vfz9cfvnlhzx///792TjRgRsAUFx97/l473vfmwWIF77whdns+jgH5C/+4i/C1VdffcjzN2zYEG688cZ+VwMAmCs9H1/+8pfD5z//+fCFL3whbN++PZv78dGPfjQrD2X9+vXZzNjJbdeuXf2uEgBQ5EdtlyxZkvV+rFu3burYhz70ofC5z30u/PjHPz7q93vUFgDyZ6CP2j799NOHfKviwa95BgDmpr7P+Vi1alU2x+Occ87JHrV96KGHwsc+9rHw9re/vd8/CgDIob4Puzz55JPZS8Y2bdoU9uzZExYtWhSuuuqq8P73vz/Mnz//qN9v2AUA8mcm92+vVwcA8j3nA5j52ivNZjMrAeYC4QMGqNFohFKpFKrValbGfYCiM+wCAxJ7OmLgOPBJsPhk2MTEhEXggNwx7AI50Gq1nvEIenwj8Pj4+MDqBJCC8AEDUqlUDvlOnHK5PLA6AaQgfMCAxKGVer2eBY4olrVazZALUHjmfMAQzP2IQy2xx0PwAPJqJvfvvr/hFJiZGDiEDmAuMewCACQlfAAASQkfAEBSwgcAkJTwAQAkJXwAAEkJHwBAUsIHAJCU8AEAJCV8wDRef95sNrMSgOMnfMARNBqNUCqVQrVazcq4D8DxsbAcHEbs6YiBo9PpTB2LK89OTExYiwXgOO7fej7gMFqtVk/wiNrtdrYCLQDHTviAw6hUKmF0tPcjEns+yuXywOoEUATCBxxGHFqp1+tZ4IhiWavVDLkAHCdzPmAacz/iUEvs8RA8AI7//j3viF8FssAhdAD0j2EXACAp4QMASEr4AACSEj4AgKSEDwAgKeEDAEhK+AAAkhI+AICkhA8AICnhAwBISvigEOL6K81mMysBGG7CB7nXaDRCqVQK1Wo1K+M+AMPLqrbkWuzpiIGj0+lMHRsbGwsTExMWgwMY0vu3ng9yrdVq9QSPqN1uh/Hx8YHVCYAjEz7ItUqlEkZHe3+NY89HuVweWJ0AODLhg1yLQyv1ej0LHFEsa7WaIReAIWbOB4WZ+xGHWmKPh+ABMNz373nJagWzKAYOoQMgHwy7AABJCR8AQFLCBwCQlPABACQlfAAASQkfAEBSwgcAkJTwAQAkJXwAAEkJHwBAUsIHydZeaTabWQnA3CZ8MOsajUYolUqhWq1mZdwHYO6alfDx85//PPzhH/5hOOOMM8KJJ54YLrjggrB169bZ+FEMudjTsWbNmtDpdLL9WK5du1YPCMAc1vdVbX/1q1+F17zmNWH58uXhW9/6Vnj2s58dWq1WOO200/r9o8iBeO0ng8ekdrsdxsfHrUILMEf1PXzcfPPNYcmSJeGzn/3s1LGlS5f2+8eQE5VKJYyOjvYEkLGxsVAulwdaLwAKNOzyta99LVx00UXhD/7gD8JznvOc8LKXvSx86lOfOuz5+/fvD3v37u3ZKI7Yu1Gv17PAEcWyVqvp9QCYw0a63W63n//ChQsXZuUNN9yQBZAHH3wwXHfddeH2228Pq1evfsb5H/zgB8ONN974jONPPPFEOOWUU/pZNQYozvGIQy2xx0PwACie2Hlw6qmnTuv+3ffwMX/+/Kzn47777ps6du2112Yh5P777z9kz0fcDqx8HLYRPgCgmOGj78MuZ599dnjxi1/cc+xFL3pR+NnPfnbI8xcsWJBV8sANACiuvoeP+KTLI4880nPsJz/5SfZ+BwCAvoePP/3TPw0PPPBA+Mu//MtsjP8LX/hCNuFw3bp1/f5RAEAO9T18vPKVrwybNm0KX/ziF8P5558fbrrppnDLLbeEq6++ut8/CgDIob5POE05YQUAGA4DnXAKAHAkwgcAkJTwAQAkJXwAAEkJH0y9/rzZbFrqHoBZJ3wQGo1G9hK4arWalXEfAGaLR23nuNjTEQPHwUveT0xMWAAOgGnzqC3T1mq1eoJH1G63s7fTAsBsED7muEqlEkZHe38NYs9HuVweWJ0AKDbhY46LQytx7Z0YOKJY1mo1Qy4AzBpzPpia+xGHWmKPh+ABwGzev+fN+N9OIcXAIXQAkIJhFwAgKeEDAEhK+AAAkhI+AICkhA8AICnhAwBISvgAAJISPgCApIQPACAp4QMASEr4yNHaK81mMysBIM+EjxxoNBqhVCqFarWalXEfAPLKqrZDLvZ0xMDR6XSmjsVl7ycmJiwEB0Au7996PoZcq9XqCR5Ru90O4+PjA6sTABwP4WPIVSqVMDrae5liz0e5XB5YnQDgeAgfQy4OrdTr9SxwRLGs1WqGXADILXM+cjT3Iw61xB4PwQOAYTOT+/e8ZLXiuMTAIXQAUASGXQCApIQPACAp4QMASEr4AACSEj4AgKSEDwAgKeEDAEhK+AAAkhI+AICkhA8AICnho8/rrzSbzawEAA5N+OiTRqMRSqVSqFarWRn3AYBnsqptH8Sejhg4Op3O1LGxsbEwMTFhMTgA5oS9M7h/6/nog1ar1RM8ona7HcbHxwdWJwAYVsJHH1QqlTA62vufMvZ8lMvlgdUJAIaV8NEHcWilXq9ngSOKZa1WM+QCAIdgzkef537EoZbY4yF4ADCX7J3B/XteslrNATFwCB0AcGSGXQCApIQPACAp4QMASEr4AACSEj4AgKSEDwAgKeEDAChW+Pjwhz8cRkZGwvXXXz/bPwoAmOvh48EHH8xeM/6Sl7xkNn8MAJAjsxY+9u3bF66++urwqU99Kpx22mlhWF5/3mw2sxIAKFj4WLduXVi5cmW47LLLjnje/v37s/fBH7jNhkajEUqlUqhWq1kZ9wGAgoSPO++8M2zfvj1s2LDhqOfGc+JCNJPbkiVL+l6f2NOxZs2a0Ol0sv1Yrl27Vg8IABQhfOzatStcd9114fOf/3xYuHDhUc9fv359tgLe5Ba/v99ardZU8JjUbrezFWgBgLT6vqrttm3bwp49e8LLX/7ynhv9li1bwq233poNs4yNjU19bcGCBdk2myqVShgdHe0JILEO5XJ5Vn8uAJCg5+PSSy8NDz/8cNixY8fUdtFFF2WTT+M/Hxg8UonL3Nfr9amfHcv4FE48DgDkvOfj5JNPDueff37PsZNOOimcccYZzzie0jXXXBNWrFiRDbXEHg/BAwAKEj6GWQwcQgcAzIHwce+996b4MQBADljbBQBISvgAAJISPgCApIQPACAp4QMASEr4AACSEj4AgKSEDwAgKeEDAEhK+AAA5vbaLt1uNyv37t076KoAANM0ed+evI/nKnw8+eSTWblkyZJBVwUAOIb7+KmnnnrEc0a604koCXU6nfDYY4+Fk08+OYyMjPQ9lcVQs2vXrnDKKaeEoil6++ZCG7Uv/4reRu3Lv72z1MYYJ2LwWLRoURgdHc1Xz0es8Gwvex//Yxf1l2outG8utFH78q/obdS+/DtlFtp4tB6PSSacAgBJCR8AQFJzKnwsWLAgfOADH8jKIip6++ZCG7Uv/4reRu3LvwVD0Mahm3AKABTbnOr5AAAGT/gAAJISPgCApIQPACCpwoWPjRs3hnPPPTcsXLgwXHLJJeGHP/zhEc//u7/7u/DCF74wO/+CCy4I3/zmN0NR2nfHHXdkb4k9cIvfN6y2bNkSVq1alb0dL9Z18+bNR/2ee++9N7z85S/PZm2Xy+WszcNspm2M7Tv4Gsbt8ccfD8Nmw4YN4ZWvfGX2duLnPOc54corrwyPPPLIUb8vT5/BY2ljnj6Ht912W3jJS14y9fKpV73qVeFb3/pWYa7fsbQxT9fvUD784Q9ndb7++uvDMF3HQoWPL33pS+GGG27IHiHavn17uPDCC8OKFSvCnj17Dnn+fffdF6666qpwzTXXhIceeij7QxK3f/u3fwtFaF8UP1y/+MUvprZHH300DKunnnoqa1MMWNOxc+fOsHLlyrB8+fKwY8eO7MP1R3/0R+Guu+4KRWnjpHiDO/A6xhvfsPne974X1q1bFx544IFw9913h9/85jfhda97Xdbmw8nbZ/BY2pinz2F8u3S8WW3bti1s3bo1VKvVcMUVV4Qf/ehHhbh+x9LGPF2/gz344IOhVqtlYetIBnIduwVy8cUXd9etWze13263u4sWLepu2LDhkOe/8Y1v7K5cubLn2CWXXNJdu3Zttwjt++xnP9s99dRTu3kUfzU3bdp0xHPe8573dM8777yeY29605u6K1as6Baljc1mMzvvV7/6VTdv9uzZk9X9e9/73mHPydtn8FjamOfPYXTaaad1P/3pTxfy+k2njXm9fk8++WS3Uql077777u5rX/va7nXXXXfYcwdxHQvT8/G///u/WZK97LLLetaJifv333//Ib8nHj/w/Cj2JBzu/Ly1L9q3b18olUrZIkJHS/d5k6frd7xe+tKXhrPPPjv83u/9XvjBD34Q8uCJJ57IytNPP72w13A6bczr57Ddboc777wz69WJQxNFvH7TaWNer9+6deuynuGDr8+wXMfChI//+q//yn6RzjzzzJ7jcf9w4+Px+EzOz1v7XvCCF4TPfOYz4atf/Wr43Oc+l60Y/OpXvzrs3r07FMHhrl9csfF//ud/QhHEwHH77beHr3zlK9kW//gtW7YsG3YbZvF3LQ6DveY1rwnnn3/+Yc/L02fwWNu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" ] @@ -100,12 +120,12 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -131,14 +151,14 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[2.4717291]\n" + "[2.56763627]\n" ] } ], @@ -157,14 +177,14 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[4.18459936]\n" + "[3.99216691]\n" ] } ], @@ -180,16 +200,16 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([2.27654582])" + "array([2.06512069])" ] }, - "execution_count": 6, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -210,14 +230,14 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "2.4717291029649546\n" + "2.5676362738874774\n" ] } ], @@ -234,16 +254,16 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "4.184599360470533" + "np.float64(3.992166911745958)" ] }, - "execution_count": 8, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -262,12 +282,12 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 11, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -294,7 +314,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -308,7 +328,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -317,12 +337,12 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -338,7 +358,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -358,16 +378,16 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([1.12539439])" + "array([0.99109086])" ] }, - "execution_count": 38, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" } @@ -376,19 +396,11 @@ "the0, the1 = MyOLS(x,y)\n", "the1" ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# TODO - Students\n", - "- [ ] Efficacy --> time: For method Vs. Numpy" - ] } ], "metadata": { "kernelspec": { - "display_name": ".venv", + "display_name": ".venv (3.9.6.final.0)", "language": "python", "name": "python3" }, @@ -402,7 +414,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.7" + "version": "3.9.6" } }, "nbformat": 4,